Dynamics of Stage-structured Population Models with Harvesting Pulses

In most models of population dynamics, changes in population due to birth or harvesting are assumed to be time-independent, but many species reproduce or are caught only during a single period of the year. In this paper a single species stage-structured model with density-dependent maturation rate, birth pulse and harvesting pulse is formulated. Using the discrete dynamical system determined by its Poincare map, the existence and stability of nonnegative equilibrium is studied. Furthermore by simulation, a detailed study of the various dynamics are made including period doubling, period halfing, intermittency, crisis, nonunique dynamics and chaotic attractors. The occurrence of these complex dynamic behaviors is related to the fact that minor changes in parameter or initial values can strikingly change the dynamic behaviors of the system. Finally, the dynamic behavior of the system is compared when μ is used as a bifurcation parameter with that when b is used. Key-Words: Stage structure, Density-dependent, Harvesting pulse, Birth pulse, Complexities.